Spatially compressed spectral proper orthogonal decomposition.

Abstract

Recovering coherent structures from sparse or partially sampled flow field data is inherently challenging, and traditional spectral proper orthogonal decomposition (SPOD) methods are further constrained by high computational cost, memory demands, and limited applicability. To mitigate incomplete experimental coverage and the computational constraints of high-fidelity simulations, this study proposes a spatially compressed SPOD (scSPOD) method to reconstruct global flow modes from spatially nonuniform datasets. The method integrates the assumption of spectral translation with clustering, compressed sensing, and optimization to directly recover SPOD modes from spatial subsets while preserving dominant spectral features. Validation is conducted using two representative cases: a direct numerical simulation of flow past a cylinder with a tonal spectrum and a large eddy simulation of tip leakage flow exhibiting broadband characteristics. In both cases, scSPOD accurately identifies the spatial structure of flow modes across the domain, while the quantitative reconstruction accuracy is notably high for first-order modes associated with low-rank behavior. A spectral concentration metric θ is introduced to quantify this property, with a threshold of θ≥0.75 that ensures high reconstruction accuracy. When this condition is satisfied, the reconstruction deviation of the first-order modes remains below 10^{-4} using only 3.03% of the cylinder flow data, and averages around 10^{-2} using 11.18% of the leakage flow data. These results confirm the feasibility and effectiveness of scSPOD and highlight its potential for low-cost, high-fidelity flow diagnostics in complex fluid systems.